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<Title>Boost Graph Library: Connected Components</Title>
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<H1>
<A NAME="sec:connected-components">
<img src="figs/python.gif" alt="(Python)"/>
<TT>connected_components</TT></A>
</H1>

<PRE>
<i>// named parameter version</i>
template &lt;class VertexListGraph, class ComponentMap, class P, class T, class R&gt;
typename property_traits&lt;ComponentMap&gt;::value_type
connected_components(VertexListGraph&amp; G, ComponentMap comp,
    const bgl_named_params&lt;P, T, R&gt;&amp; params = <i>all defaults</i>);

<i>// there is not a non-named parameter version of this function</i>
</PRE>

<P>
The <TT>connected_components()</TT> functions compute the connected
components of an undirected graph using a DFS-based approach.  A
<b><I>connected component</I></b> of an undirected graph is a set of
vertices that are all reachable from each other. If the connected
components need to be maintained while a graph is growing the
disjoint-set based approach of function <a
href="./incremental_components.html">
<TT>incremental_components()</TT></a> is faster. For ``static'' graphs
this DFS-based approach is faster&nbsp;[<A
HREF="bibliography.html#clr90">8</A>].

<P>
The output of the algorithm is recorded in the component property map
<TT>comp</TT>, which will contain numbers giving the component number
assigned to each vertex. The total number of components is the return
value of the function.

<H3>Where Defined</H3>

<P>
<a href="../../../boost/graph/connected_components.hpp"><TT>boost/graph/connected_components.hpp</TT></a>


<h3>Parameters</h3>

IN: <tt>const Graph&amp; g</tt>
<blockquote>
An undirected graph. The graph type must be a model of <a
href="VertexListGraph.html">Vertex List Graph</a> and <a
href="IncidenceGraph.html">Incidence Graph</a>.<br>

<b>Python</b>: The parameter is named <tt>graph</tt>.
</blockquote>

OUT: <tt>ComponentMap c</tt>
<blockquote>
The algorithm computes how many connected components are in the graph,
and assigning each component an integer label. The algorithm then
records which component each vertex in the graph belongs to by
recording the component number in the component property map. The
<tt>ComponentMap</tt> type must be a model of <a
href="../../property_map/doc/WritablePropertyMap.html">Writable Property
Map</a>. The value type should be an integer type, preferably the same
as the <tt>vertices_size_type</tt> of the graph. The key type must be
the graph's vertex descriptor type.<br>

  <b>Python</b>: Must be an <tt>vertex_int_map</tt> for the graph.<br>
  <b>Python default</b>: <tt>graph.get_vertex_int_map("component")</tt>
</blockquote>

<h3>Named Parameters</h3>

UTIL: <tt>color_map(ColorMap color)</tt>
<blockquote>
  This is used by the algorithm to keep track of its progress through
  the graph. The type <tt>ColorMap</tt> must be a model of <a
  href="../../property_map/doc/ReadWritePropertyMap.html">Read/Write
  Property Map</a> and its key type must be the graph's vertex
  descriptor type and the value type of the color map must model
  <a href="./ColorValue.html">ColorValue</a>.<br>
  <b>Default:</b> an <a
  href="../../property_map/doc/iterator_property_map.html">
  </tt>iterator_property_map</tt></a> created from a
  <tt>std::vector</tt> of <tt>default_color_type</tt> of size
  <tt>num_vertices(g)</tt> and using the <tt>i_map</tt> for the index
  map.<br>
  <b>Python</b>: The color map must be a <tt>vertex_color_map</tt> for
  the graph.
</blockquote>

IN: <tt>vertex_index_map(VertexIndexMap i_map)</tt>
<blockquote>
  This maps each vertex to an integer in the range <tt>[0,
  num_vertices(g))</tt>. This parameter is only necessary when the
  default color property map is used. The type <tt>VertexIndexMap</tt>
  must be a model of <a
  href="../../property_map/doc/ReadablePropertyMap.html">Readable Property
  Map</a>. The value type of the map must be an integer type. The
  vertex descriptor type of the graph needs to be usable as the key
  type of the map.<br>

  <b>Default:</b> <tt>get(vertex_index, g)</tt>.
    Note: if you use this default, make sure your graph has
    an internal <tt>vertex_index</tt> property. For example,
    <tt>adjacency_list</tt> with <tt>VertexList=listS</tt> does
    not have an internal <tt>vertex_index</tt> property.<br>

  <b>Python</b>: Unsupported parameter.
</blockquote>


<H3>Complexity</H3>

<P>
The time complexity for the connected components algorithm is also
<i>O(V + E)</i>.

<P>

<h3>See Also</h3>

<a href="./strong_components.html"><tt>strong_components()</tt></a>
and <a href="./incremental_components.html"><tt>incremental_components()</tt></a>

<H3>Example</H3>

<P>
The file <a
href="../example/connected_components.cpp"><tt>examples/connected_components.cpp</tt></a>
contains an example of calculating the connected components of an
undirected graph.

<br>
<HR>
<TABLE>
<TR valign=top>
<TD nowrap>Copyright &copy; 2000-2001</TD><TD>
<A HREF="http://www.boost.org/people/jeremy_siek.htm">Jeremy Siek</A>, Indiana University (<A HREF="mailto:jsiek@osl.iu.edu">jsiek@osl.iu.edu</A>)
</TD></TR></TABLE>

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